Timeline for Is 'the' homotopy colimit of a sequence of exact triangles an exact triangle?

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when toggle format	what		by	license	comment
Jun 26, 2014 at 9:05	vote	accept	user8463524
Mar 10, 2014 at 9:36	vote	accept	user8463524
Mar 10, 2014 at 9:36
Mar 9, 2014 at 23:21	history	migrated			from math.stackexchange.com (revisions)
Mar 3, 2014 at 13:29	comment	added	Aaron Chan		Thank you for the explanation! This is something nice to know about.
Mar 3, 2014 at 11:40	comment	added	Jeremy Rickard		@Aaron: In the example of a derived category (where a short exact sequence in the category of complexes gives rise to an exact triangle in the derived category, and the colimit in the category of complexes of a direct system is isomorphic to the homotopy colimit in the derived category) then if $A_\to B_\to C_$ is a direct system of exact triangles in the derived category, there is a direct system $0\to \tilde{A}_\to \tilde{B}_\to \tilde{C}_\to 0$ of short exact sequences of complexes that gives rise to a direct system in the derived category isomorphic to $A_\to B_\to C_*$.
Mar 2, 2014 at 16:17	comment	added	Aaron Chan		I am sorry I am slightly confused, do you mean that in certain nice triangulated categories, if we can make the triangles $(A_\to B_\to C_)$ into a direct system, then $\varinjlim ( A_\to B_\to C_)$ is isomorphic to $\mathrm{hocolim}(A_) \to \mathrm{hocolim}(B_) \to \mathrm{hocolim}(C_*)$?
Mar 1, 2014 at 13:47	history	answered	Jeremy Rickard	CC BY-SA 3.0